Export keyframes as baked meshes?
You may get away with


Scene.frame_set
bpy.ops.export_scene.fbx


I.e. select your meshes and run

import bpy

PATH = "your_path.%03d.fbx"

for i in range(100):
    bpy.context.scene.frame_set(i)
    bpy.ops.export_scene.fbx(
        filepath=PATH % i,
        object_types={'MESH'},
        use_selection=True
        )


The source code of export_scene.fbx resides in scripts/addons/io_scene_fbx.